Critical angle of glass is `theta_(1)` and that of water is `theta_(2)`. The critical angle for water and glass surface would be `(mu_(g)=3//2, mu_(w)=4//3)`

Options

A. less than `theta_(2)`
B. between `theta_(1)` and `theta_(2)`
C. greater than `theta_(2)`
D. less than `theta_(1)`

Explanation

To find the critical angle for the interface between water and glass, we can use the formula for critical angle in terms of refractive indices. The critical angle (θ) can be calculated using the formula:

\[ \sin \theta = \frac{\mu_w}{\mu_g} \]

where:
- \(\mu_w\) is the refractive index of water,
- \(\mu_g\) is the refractive index of glass.

Given:
- \(\mu_g = \frac{3}{2}\)
- \(\mu_w = \frac{4}{3}\)

### Step 1: Write the formula for the critical angle
The formula for the critical angle when light travels from a medium with a lower refractive index (water) to a medium with a higher refractive index (glass) is:

\[ \sin \theta = \frac{\mu_w}{\mu_g} \]

### Step 2: Substitute the values of refractive indices
Substituting the given values into the formula:

\[ \sin \theta = \frac{4/3}{3/2} \]

### Step 3: Simplify the fraction
To simplify the fraction, we can multiply by the reciprocal of the denominator:

\[ \sin \theta = \frac{4}{3} \times \frac{2}{3} = \frac{8}{9} \]

### Step 4: Find the critical angle
Now, to find the critical angle θ, we take the inverse sine (arcsin) of \(\frac{8}{9}\):

\[ \theta = \arcsin\left(\frac{8}{9}\right) \]

### Step 5: Conclusion
The critical angle for the water and glass interface is given by:

\[ \theta = \arcsin\left(\frac{8}{9}\right) \]